Reducing the parameterization of the covariance matrix for maximum likelihood classification

Hyperspectral, remotely sensed data generate very large covariance matrices and this has a significant impact on the computational load and processing time. As the dimensionality of the data increases, so to does the number of training samples required to estimate the covariance matrices of the data. Two approaches for significantly reducing the number of parameters needed to represent a covariance matrix are presented and these are applied to data acquired by the HyMap sensor. The inverse covariance matrix for hyperspectral data is typically sparse and can be approximated as band-diagonal. A good approximation of the covariance matrix has been achieved using only a fraction of the number of parameters.